If you mean (1+2x)2, that is already factored.
(x + 1)(2x + 5)
(2x + 1)(x + 2)
OK. 4x2 + 4x + 1 = (2x + 1)2
(x - 1)(2x - 9)
(2x - 1)(2x + 5)
(2x-3)(x-1)
x(x + 2)
The answer is (2x^2+3)(4x+1)
There is no rational factorisation.
(4x + 1)(2x + 3)
4
(2x-1)(2x-1) = 4x^2 -4x + 1